Poor gas mileage

One thing, the prius will report higher fuel economy than it actually gets. The best way is to simply use your trip odometer and record the mileage and get your receipts from the gas station. I'd run about 3 tanks of gas through just for good measure.

Not sure what everyone else does when they get gas. I stop filling when the pump stops, I don't try to jam as much as possible in, this way, it doesn't make the fuel economy appear worse than it really is. While mine is a 4th gen, the same applies, they're about 5-8% optimistic on gas mileage. So if it says you're getting 52, you should be getting 47-49 MPG.

As far as the battery, yes, it could be a problem for a 12 year old Prius with a good bit of mileage. You can have the battery tested or if you're more of a techie you can get a OBD II reader (Wifi Dongle's often are pretty cheap and work reasonably well) and test the battery yourself for a lot cheaper than going to a dealer. If you're not a a "techie" or want to deal with the hassles of buy apps, pairing bluetooth/WiFi with your phone/tablet, etc, then do take it somewhere and have it checked.

The not so bad news is that even if the battery shows weak cells, it doesn't mean the car is destined to the junkyard. Often you can have someone replace the weak/bad cells and the cost is much much less than replacing the entire battery.

The other thing I would be wondering is whether or not you have a check engine light on, if it is on after replacing the gas cap and experiencing poor fuel economy there could be one or several things causing that.

 

where did you get the gas cap? i would go back and tell them what happened. they need to replace it under warranty.

 

"how many times I'm having to fill up" isn't relevant to this issue. What MPG are you actually getting at the gas pump, computed as miles between fillups divided by fuel delivered in the fillups? (If you don't keep track of fuel quantity purchased, then you don't yet have any basis for an MPG complaint.)

Too-early refill needs are often caused by the Gen2's finicky gas tank bladder, more often a problem in cold weather. But those refills should also be for smaller amounts of fuel, not hurting MPG in itself. (Though winter conditions due hurt MPG for completely different reasons.)

 

Fuel economy is a mathematical calculation and does not revolve on how often you fill up (tank size or vehicle range), but on how many gallons (or liters) of fuel consumed over the distance traveled.

The fuel gauges in Gen2 Prii are notoriously inaccurate at anything over 1/4 tank.

I suspect the fuel tank is not venting correctly due to the newly installed cap. It is a simple matter for a qualified shop to check the fuel tank vent system to ensure it is working correctly.